A theoretical investigation is performed into the electroviscous-induced retardation of liquid flows through finitely long nanochannels or nanotubes with large wells at either end. Given the assumption of equilibrium conditions between the ionic solution in the wells and that within the nanochannel or nanotube, an exact solution is derived for the overlapped electrical double layer (EDL) for the case where the concentrations of the positive and negative ions in the wells may be unequal. The ion concentrations in the wells are determined by the conditions of global electroneutrality and mass conservation. It is shown that the overlapped EDL model proposed by Baldessari and Santiago [J. Colloid Interface Sci.325, 526 (2008)10.1016/j.jcis.2008.06.007] is in fact the same as the "thick EDL model" (i.e., the traditional Poisson-Boltzmann model) when the positive and negative ion concentrations in the large enough wells are both equal to the bulk concentration of the salt solution. Utilizing the proposed overlapped EDL analytical model, an investigation is performed to evaluate the effects of hydrodynamic slippage on the flow retardation caused by electroviscosity in nanochannels or nanotubes. Furthermore, exact and approximate solutions are derived for the electroviscosity in ion-selective nanochannels and nanotubes. It is shown that in the absence of slip, the maximum electroviscosity in nanochannels and nanotubes containing a unipolar solution of simple monovalent counter-ions occurs at surface charge densities of hσ| = 0.32 nm × C/m2 and a|σ| ≈ 0.4 nm × C/m2, respectively. In addition, it is shown that the electroviscosity in a nanotube is smaller than that in a nanochannel. For example, given a LiCl solution, the maximum electroviscosites in a non-slip nanochannel and non-slip nanotube are na/n ≈ 1.6 and 1.47, respectively. For both nanospaces, the electroviscosity is greatly increased when the liquid slip effect is taken into account. Significantly, under slip conditions, the electroviscosity in the nanotube is greater than that in the nanochannel. Finally, an investigation is performed into the effects of ambient atmospheric CO2 dissolution on the electroviscosities of salt/buffer solution and deionized (DI) water in silica nanochannels. The results show that the electroviscosity of CO2-saturated DI water (pH = 5.6) can be reasonably neglected in silica nanochannels with a height of less than 100 nm.
All Science Journal Classification (ASJC) codes
- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes